I teach AP Calculus to students who, last year, did well in a rather limited Algebra II course* and who have not had pre-calculus. When faced with a question like (2007 AB FRQ4):

A particle moves along the x-axis with position at time t given by x(t)=e^{-t}\sin t for 0\le t\le 2\pi. Find the time t at which the particle is farthest from the left,

they get hung up on things like:

  • Is e^{-t} like e^x?
  • If the particle is on the x-axis, then is t on the y-axis?

They know how to differentiate the function and how to find a minimum, they just don’t know that this is what they need to do.

* The Algebra II course I am teaching this year is similarly limited – more on that another time.

PS A thousand blessings on whoever decided to put \LaTeX into wordpress.

PPS Anyone know how I can get the inline formulas more inline?